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An analysis of the boundary layer in the 1D surface Cauchy–Born model

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is &#x1d4aa;(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...

An analysis of the boundary layer in the 1D surface Cauchy–Born model∗

ESAIM: Mathematical Modelling and Numerical Analysis

The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...

An energy conserving modification of numerical methods for the integration of equations of motion.

International Journal of Mathematics and Mathematical Sciences

Analysis of a quasicontinuum method in one dimension

ESAIM: Mathematical Modelling and Numerical Analysis

The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long-range interactions and a QC formulation which incorporates several important aspects of practical QC methods. First, we prove the existence, the local uniqueness...

Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method.

Mathematical Problems in Engineering

Error estimates for the Coupled Cluster method

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...

Integrator for Lagrangian dynamics.

Balkan Journal of Geometry and its Applications (BJGA)

Kam kráčí výpočtová mechanika?

Pokroky matematiky, fyziky a astronomie

Recent progress in the integration of Poisson systems via the mid-point rule and Runge-Kutta algorithm.

Balkan Journal of Geometry and its Applications (BJGA)

Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum

Annales de l'I.H.P. Physique théorique

Simple orbit determination using GPS based on a least-squares algorithm employing sequential Givens rotations.

Mathematical Problems in Engineering

Stochastic finite element technique for stochastic one-dimensional time-dependent differential equations with random coefficients.

Differential Equations &amp; Nonlinear Mechanics

Sul collasso di un ammasso di materia disgregata. Nota I

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Starting from the considerations developed in [4], it is shown that the only forces at a distance exerted among the elements of an isolated spherical cluster of incoherent matter which, preserving homogeneity, is collapsing are those expressed by Newton's law of gravitation and those of the elastic type. Furthermore the reverse is shown, that is if the forces at a distance are of these two types during the collapse the homogeneity is preserved.

Sul collasso di un ammasso di materia disgregata. Nota II

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

With reference to Nota I, the hypothesis that the cluster $\mathcal{U}$ is spherical is substituted by the hypothesis that it has an isotropic behaviour with respect to a given frame of reference $\mathcal{I}_{O}$ with origin in an element $O$ internal to $\mathcal{U}$. The kinematical behaviour of $\mathcal{U}$ during the collapse with respect to the frames of reference with origin in the elements of $\mathcal{U}$ and in translatory motion with respect to $\mathcal{I}_{O}$ is studied. This behaviour is the same with respect to each of such frames, which are in translatory motion...

Symplectic phase flow approximation for the numerical integration of canonical systems.

Numerische Mathematik

The continuous Coupled Cluster formulation for the electronic Schrödinger equation

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the stationary electronic Schrödinger equation. Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, i.e. within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis...

The Helmholtz conditions for the difference equations systems.

Balkan Journal of Geometry and its Applications (BJGA)

Towards Sub-cellular Modeling with Delaunay Triangulation

Mathematical Modelling of Natural Phenomena

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...

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